Sparsity optimized separation of Ground-roll noise based on morphological diversity of seismic waveform components

Real seismic signals can usually be represented as a linear combination of multiple basic waveforms of different morphological characteristics, such as powerline single frequency interference noise and effective seismic signal, ground roll and body wave signals. By selecting a single mathematical transformation method, it will hard to achieve sparse representations of seismic signals. Morphological component analysis (MCA) theory has been developed in recent years, which can sparsely decompose complex signals through the augmented dictionary of basic mathematical transformations. According to the waveform divergence of ground-roll and body wave signals, this paper proposes a ground-roll attenuation method based on the morphological component analysis theory. To match with the requirements of the MCA, the 1D stationary wavelet transform (SWT) is chosen as the sparse representation dictionary of ground-roll due to its low frequency and narrow spectral bandwidth nature. Meanwhile, the local discrete cosine transform (LDCT) is chosen as the sparse representation dictionary of body waves due to its local interdependency characteristics. The optimization model on basis of the MCA is then built on the two amalgamated dictionaries and properly solved to obtain the final signal-noise separation results. The theoretical and real data processing results confirm that the method can not only attenuate strong ground-roll noise in seismic records but also preserves the waveform characteristics and spectral bandwidth of effective signal well. The method can provide high quality data for subsequent processing and analysis.